I don't care what people say, there is no free lunch .. a 7rsaum in a 20" barrel will not shoot a 180 the same speed as a 28 Nosler in a 20" barrel.
Don't know the 338s all that well but about a decade ago we did extensive work with 7s to test some theories.
At the time there was an outfit selling what I'm assuming we're rejects from savage of various different barrels. Priced 45-85 and cheaper if you bought a bunch. Some were raw length some were what appeared to be factory tapers. My wife was tasked with being familiarized with some software that was going to be used for a grad school research project. They wanted her to pick something arbitrary that she understood to learn the software on. She was devoid of ideas so I bought a bunch of seven Ultra Mag and 270 short mag cheapie barrels, and started chopping them down.
Eventually we rotated in a 7 mag barrel that I was given and a takeoff 7 wsm barrel a buddy gave me from a 6.5wsm project.
We learned several things. Barrel velocity loss isn't linear across 16-26 inches, it's also not the same across bullet weight options. Heavy and light for caliber always dropped off more than middle of the road options... eg a 110 grain v max would loose more on average in a short barrel than a 130 or 140 in A 270 wsm as would a 160, but it was way more pronounced when we used 85grain e tips.
The big takeaway was as mentioned above, boiler room matters most. With a caveat of course. We didn't go below 16 inches on our test, although a friend with a striker did take the 27p wsm to 10 inches. A 20 inch 7 rum will beat a 7 mag or 7 wsm that's also 20 inches, but with all starting at 26 the percentage of win gets lower and lower. Stack a 7 rum next to a 7wsm next to each other, the rum has a perceptible amount of less usable barrel length. We found that the 270 and 7 wsm cartridges dropped minimally per inch from 26 to 21, modestly from 21 to 19 and kinda off a cliff from 16 to 19. In fps metrics were talking 25 to 35 fps per inch 21 to 26, 35-40 in the 19-21 inch range and 60-80 fps below 19.
The 7 rum showed the same significant drop around 21 or 22 inches, (our modeling was almost exactly 21 5/8 for my preferred hunting bullet)
In all lengths 16 to 26, the 7 rum stomped the 7 wsm.
Side observations,
Xp hunter Ernie was right. Powder speed did not have an effect on velocity loss. The fastest load long was fastest short, I'd thought it was not so but a friend who knows numbers and looked at the data politely pointed out withing normal rifle configuration and use the powder burn differences would not equate to differences distinguished with over the counter measuring devices.
I've no doubt the intangible aspects of more mild cartridges have merit. My 18 inch 7 wsm could cook and well as kill something with its fireball.